Q3. [20 pts] (a) [6 pts) Find the quadratic spline denoted by p(t) on (-1, 1) with a knot at t = 0; such that p(t) = 0,Vt (-1,0), and p(1) = 1. (b) (7 pts) Consider p(t) = 20 + a1t+ a2ta +a3p(t) with 20, 21, 22, az R, and p(t) given in (a). Classify p(t) as an interpolating function. Determine p(t) so that p(-1) = f(-1), p(0) = f(0), p'0) = f'(o), p(1) = f(1), for some function f e C?(-1,1]. (c) (7 pts) Assuming that p(t) = f(t) on t (-1,1], where plt) is obtained in (b); construct a quadrature rule to approximate L-, f(t)dt. Which quadrature rule is this? 3Piecewise polynomial of degree 2 Q3. [20 pts] (a) [6 pts) Find the quadratic spline denoted by p(t) on (-1, 1) with a knot at t = 0; such that p(t) = 0,Vt (-1,0), and p(1) = 1. (b) (7 pts) Consider p(t) = 20 + a1t+ a2ta +a3p(t) with 20, 21, 22, az R, and p(t) given in (a). Classify p(t) as an interpolating function. Determine p(t) so that p(-1) = f(-1), p(0) = f(0), p'0) = f'(o), p(1) = f(1), for some function f e C?(-1,1]. (c) (7 pts) Assuming that p(t) = f(t) on t (-1,1], where plt) is obtained in (b); construct a quadrature rule to approximate L-, f(t)dt. Which quadrature rule is this? 3Piecewise polynomial of degree 2